April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
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Summary and Notes
The chapters in this part describe several order-recursive (lattice) implementations of RLS.
SUMMARY OF MAIN RESULTS
- The lattice forms are primarily concerned with order-updating the output estimation error and not the weight vector itself. To do so, forward and backward prediction errors also need to be order-updated.
- All order-update relations derived in the chapter hold irrespective of data structure. As indi cated in Fig. 41.1, the only place where the structure of the regressors is relevant is in knowing how to generate the error quantities
from the error quantities bM(i): both these errors are related to backward projection problems. - When the regressors possess shift structure, it holds that
There are situations where the regressors are not shifted versions of each other and yet one can still relate 
— see, e.g., Chapter 16 of Sayed (2003) on Laguerre lattice filters and Merched and Sayed (2000b,2001a). - Seven lattice forms are described in the text: (a) a posteriori lattice form, (b) a priori lattice form, (c) a priori lattice form with error feedback, (d) a posteriori lattice form with error feedback, (e) normalized lattice form, (f) array lattice form, ...
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